Finite Group Databasebeta

← C2×#24912371 #35575668

Subgroups — C2×#24912371 #35575668

Order 21248.

3526 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14581770C211yesmaximal, characteristic, complemented
2C22×#14581769C211yesmaximal, characteristic, complemented
3C22×C4×Dic166C211yesmaximal, characteristic, complemented
4C22×(C22⋊D83)⋊C4C211yesmaximal, characteristic
5#24912371C2116yesmaximal, direct product factor
6C2×#19127635C211yesmaximal, characteristic, complemented
7C2×#19127634C211yesmaximal, characteristic, complemented
8C2×#19127617C211yesmaximal, characteristic
9C2×#19127616C211yesmaximal, characteristic
10C2×#19127593C211yesmaximal, characteristic, complemented
11C2×#19127592C211yesmaximal, characteristic, complemented
12C2×#19127589C211yesmaximal, characteristic, complemented
13C2×#19127565C211yesmaximal, characteristic, complemented
14C2×#19127560C211yesmaximal, characteristic, complemented
15C2×#19127559C211yesmaximal, characteristic, complemented
16C2×#388×C83C211yesmaximal, characteristic, complemented
17C23×Dic166C2211yescharacteristic
18C23×C22⋊D83C2211yescharacteristic
19C24×Dic83C2211yescharacteristic
20C23×C4×D83C2211yescharacteristic
21C2×#14581770—28no—
22C2×#14581770C2218yescomplemented
23C2×#14581769—28no—
24C2×#14581769C2218yescomplemented
25C2×C4×Dic166—28no—
26C2×C4×Dic166C2218yescomplemented
27C2×(C22⋊D83)⋊C4—28no—
28C2×(C22⋊D83)⋊C4C2218yes—
29C22×C4⋊Dic83C2211yescharacteristic
30C22×C4⋊Dic83C2211yescharacteristic
31C22×Dic83⋊C4C2211yescharacteristic
32C22×Dic83⋊C4C2211yescharacteristic
33C22×Dic83⋊C4C2211yescharacteristic
34C22×Dic83⋊C4C2211yescharacteristic
35C22×Dic83⋊C4C2211yescharacteristic
36C22×Dic83⋊C4C2211yescharacteristic
37C22×Dic83⋊C4C2211yescharacteristic
38C22×C22⋊Dic83C2211yescharacteristic
39C22×C22⋊Dic83C2211yescharacteristic
40C22×(C2×D83)⋊C4C2211yescharacteristic
41C22×(C2×D83)⋊C4C2211yescharacteristic
42C22×(C2×D83)⋊C4C2211yescharacteristic
43C22×(C2×D83)⋊C4C2211yescharacteristic
44C22×(C2×D83)⋊C4C2211yescharacteristic
45C22×C4×Dic83C2211yescharacteristic
46C22×C4×Dic83C2211yescharacteristic
47#19127635C2218yescomplemented
48#19127634C2218yescomplemented
49#19127617C2218yes—
50#19127616C2218yes—
51#19127593C2218yescomplemented
52#19127592C2218yescomplemented
53#19127589C2218yescomplemented
54#19127565C2218yescomplemented
55#19127560C2218yescomplemented
56#19127559C2218yescomplemented
57C2×C83⋊#95C2211yescharacteristic
58C2×C83⋊#95C2211yescharacteristic
59C2×C83⋊#95C2211yescharacteristic
60C2×C83⋊#95C2211yescharacteristic
61C2×C83⋊#95C2211yescharacteristic
62C2×C83⋊#95C2211yescharacteristic
63C22×C4⋊C4×C83C2211yescharacteristic
64C22×C22⋊C4×C83C2211yescharacteristic
65C22×C22⋊C4×C83C2211yescharacteristic
66C22×C22⋊C4×C83C2211yescharacteristic
67C22×C42×C83C2211yescharacteristic
68#388×C83C2218yescomplemented
69C2×#95×C83C2211yescharacteristic
70C2×#95×C83C2211yescharacteristic
71C24×D83C2311yescharacteristic
72C22×Dic166—24no—
73C22×Dic166—24no—
74C22×Dic166D418yescomplemented
75C22×Dic166C2314yes—
76C22×C22⋊D83—24no—
77C22×C22⋊D83—24no—
78C22×C22⋊D83—24no—
79C22×C22⋊D83C2314yes—
80C23×Dic83—24no—
81C23×Dic83—24no—
82C23×Dic83—24no—
83C23×Dic83C2314yes—
84C23×Dic83C2311yescharacteristic
85C23×Dic83C2311yescharacteristic
86C23×Dic83C2311yescharacteristic
87C23×Dic83C2311yescharacteristic
88C23×Dic83C2311yescharacteristic
89C23×Dic83C2311yescharacteristic
90C23×Dic83C2311yescharacteristic
91C22×C4×D83—24no—
92C22×C4×D83—24no—
93C22×C4×D83—24no—
94C22×C4×D83C2314yes—
95#14581770—232no—
96#14581769—232no—
97C4×Dic166—232no—
98(C22⋊D83)⋊C4—232no—
99C2×C4⋊Dic83—24no—
100C2×C4⋊Dic83—24no—
101C2×C4⋊Dic83C2314yes—
102C2×C4⋊Dic83C2314yes—
103C2×Dic83⋊C4—24no—
104C2×Dic83⋊C4—24no—
105C2×Dic83⋊C4—24no—
106C2×Dic83⋊C4—24no—
107C2×Dic83⋊C4—24no—
108C2×Dic83⋊C4—24no—
109C2×Dic83⋊C4—24no—
110C2×Dic83⋊C4C2314yes—
111C2×Dic83⋊C4C2314yes—
112C2×Dic83⋊C4C2314yes—
113C2×Dic83⋊C4C2314yes—
114C2×Dic83⋊C4C2314yes—
115C2×Dic83⋊C4C2314yes—
116C2×Dic83⋊C4C2314yes—
117C2×C22⋊Dic83—24no—
118C2×C22⋊Dic83—24no—
119C2×C22⋊Dic83C2314yes—
120C2×C22⋊Dic83C2314yes—
121C2×(C2×D83)⋊C4—24no—
122C2×(C2×D83)⋊C4—24no—
123C2×(C2×D83)⋊C4—24no—
124C2×(C2×D83)⋊C4—24no—
125C2×(C2×D83)⋊C4—24no—
126C2×(C2×D83)⋊C4C2314yes—
127C2×(C2×D83)⋊C4C2314yes—
128C2×(C2×D83)⋊C4C2314yes—
129C2×(C2×D83)⋊C4C2314yes—
130C2×(C2×D83)⋊C4C2314yes—
131C2×C4×Dic83—24no—
132C2×C4×Dic83D418yes—
133C2×C4×Dic83C2314yes—
134C2×C4×Dic83C2314yes—
135C83⋊#95C2314yes—
136C83⋊#95C2314yes—
137C83⋊#95C2314yes—
138C83⋊#95C2314yes—
139C83⋊#95C2314yes—
140C83⋊#95C2314yes—
141C25×C83C2311yescharacteristic
142C23×C4×C83C2311yescharacteristic
143C23×C4×C83C2311yescharacteristic
144C23×C4×C83C2311yescharacteristic
145C23×C4×C83C2311yescharacteristic
146C23×C4×C83C2311yescharacteristic
147C23×C4×C83C2311yescharacteristic
148C2×C4⋊C4×C83—24no—
149C2×C4⋊C4×C83C2314yes—
150C2×C22⋊C4×C83—24no—
151C2×C22⋊C4×C83—24no—
152C2×C22⋊C4×C83—24no—
153C2×C22⋊C4×C83C2314yes—
154C2×C22⋊C4×C83C2314yes—
155C2×C22⋊C4×C83C2314yes—
156C2×C42×C83—24no—
157C2×C42×C83C2314yes—
158#95×C83C2314yes—
159#95×C83C2314yes—
160C23×D83—22no—
161C23×D83—22no—
162C23×D83—22no—
163C23×D83—22no—
164C23×D83—22no—
165C23×D83—22no—
166C23×D83#4114yes—
167C23×D83C2412yes—
168C2×Dic166—232no—
169C2×Dic166—28no—
170C2×Dic166—28no—
171C2×Dic166C2×D4116yescomplemented
172C2×C22⋊D83—232no—
173C2×C22⋊D83—28no—
174C2×C22⋊D83—28no—
175C2×C22⋊D83—28no—
176C22×Dic83—22no—
177C22×Dic83—22no—
178C22×Dic83—22no—
179C22×Dic83—22no—
180C22×Dic83—22no—
181C22×Dic83—22no—
182C22×Dic83—22no—
183C22×Dic83—22no—
184C22×Dic83—22no—
185C22×Dic83—22no—
186C22×Dic83—22no—
187C22×Dic83—22no—
188C22×Dic83—22no—
189C22×Dic83—22no—
190C22×Dic83—22no—
191C22×Dic83—22no—
192C22×Dic83—28no—
193C22×Dic83—28no—
194C22×Dic83—28no—
195C22×Dic83—416no—
196C22×Dic83C2×D414yes—
197C22×Dic83C2×D414yes—
198C22×Dic83C2×D414yes—
199C22×Dic83C2×D414yes—
200C22×Dic83#4114yes—
201C22×Dic83C2412yes—
202C22×Dic83C2412yes—
203C22×Dic83C2412yes—
204C22×Dic83C2412yes—
205C22×Dic83C2412yes—
206C22×Dic83C2412yes—
207C22×Dic83C2412yes—
208C2×C4×D83—28no—
209C2×C4×D83—28no—
210C2×C4×D83—28no—
211C2×C4×D83—416no—
212C4⋊Dic83—28no—
213C4⋊Dic83—28no—
214Dic83⋊C4—28no—
215Dic83⋊C4—28no—
216Dic83⋊C4—28no—
217Dic83⋊C4—28no—
218Dic83⋊C4—28no—
219Dic83⋊C4—28no—
220Dic83⋊C4—28no—
221C22⋊Dic83—28no—
222C22⋊Dic83—28no—
223(C2×D83)⋊C4—28no—
224(C2×D83)⋊C4—28no—
225(C2×D83)⋊C4—28no—
226(C2×D83)⋊C4—28no—
227(C2×D83)⋊C4—28no—
228C4×Dic83—28no—
229C4×Dic83C2×D4116yes—
230C24×C83—22no—
231C24×C83—22no—
232C24×C83—22no—
233C24×C83—22no—
234C24×C83—22no—
235C24×C83—22no—
236C24×C83#4114yes—
237C24×C83C2412yes—
238C24×C83C2411yescharacteristic
239C22×C4×C83—22no—
240C22×C4×C83—22no—
241C22×C4×C83—22no—
242C22×C4×C83—22no—
243C22×C4×C83—22no—
244C22×C4×C83—22no—
245C22×C4×C83—22no—
246C22×C4×C83—22no—
247C22×C4×C83—22no—
248C22×C4×C83—22no—
249C22×C4×C83—22no—
250C22×C4×C83—22no—
251C22×C4×C83—22no—
252C22×C4×C83—22no—
253C22×C4×C83—22no—
254C22×C4×C83—22no—
255C22×C4×C83C2×D414yes—
256C22×C4×C83C2×D414yes—
257C22×C4×C83C2412yes—
258C22×C4×C83C2412yes—
259C22×C4×C83C2412yes—
260C22×C4×C83C2412yes—
261C22×C4×C83C2412yes—
262C22×C4×C83C2412yes—
263C4⋊C4×C83—28no—
264C22⋊C4×C83—28no—
265C22⋊C4×C83—28no—
266C22⋊C4×C83—28no—
267C42×C83—28no—
268C23×C83—28no—
269C23×C83—28no—
270C23×C83—28no—
271C23×C83—22no—
272C23×C83—22no—
273C23×C83—22no—
274C23×C83—22no—
275C23×C83—22no—
276C23×C83—22no—
277C23×C83—44no—
278C23×C83—44no—
279C23×C83—44no—
280C23×C83—44no—
281C23×C83C22×D412yes—
282C23×C83C22×D412yes—
283C23×C83C2×#4112yes—
284C23×C83C2×#4112yes—
285C23×C83C2×#4114yes—
286C23×C83C2×#4112yes—
287C23×C832−1+412yes—
288C23×C832−1+412yes—
289C23×C83C2511yescharacteristic
290C22×D83—28no—
291C22×D83—28no—
292C22×D83—28no—
293C22×D83—22no—
294C22×D83—22no—
295C22×D83—22no—
296C22×D83—22no—
297C22×D83—22no—
298C22×D83—22no—
299C22×D83—44no—
300C22×D83—44no—
301C22×D83—44no—
302C22×D83—44no—
303C22×D83C2×#4114yes—
304C2×C4×C83—28no—
305C2×C4×C83—28no—
306C2×C4×C83—22no—
307C2×C4×C83—22no—
308C2×C4×C83—22no—
309C2×C4×C83—22no—
310C2×C4×C83—22no—
311C2×C4×C83—22no—
312C2×C4×C83—22no—
313C2×C4×C83—22no—
314C2×C4×C83—22no—
315C2×C4×C83—22no—
316C2×C4×C83—22no—
317C2×C4×C83—22no—
318C2×C4×C83—22no—
319C2×C4×C83—22no—
320C2×C4×C83—22no—
321C2×C4×C83—22no—
322C2×C4×C83—44no—
323C2×C4×C83—44no—
324C2×C4×C83—44no—
325C2×C4×C83—44no—
326C2×C4×C83C22×D414yes—
327C2×C4×C83C22×D414yes—
328C22⋊D83—232no—
329C2×Dic83—28no—
330C2×Dic83—28no—
331C2×Dic83—22no—
332C2×Dic83—22no—
333C2×Dic83—22no—
334C2×Dic83—22no—
335C2×Dic83—22no—
336C2×Dic83—22no—
337C2×Dic83—22no—
338C2×Dic83—22no—
339C2×Dic83—22no—
340C2×Dic83—22no—
341C2×Dic83—22no—
342C2×Dic83—22no—
343C2×Dic83—22no—
344C2×Dic83—22no—
345C2×Dic83—22no—
346C2×Dic83—22no—
347C2×Dic83—44no—
348C2×Dic83—44no—
349C2×Dic83—44no—
350C2×Dic83—44no—
351C2×Dic83—416no—
352C2×Dic83#121116yes—
353C2×Dic83C22×D414yes—
354C2×Dic83C22×D414yes—
355C2×Dic83C22×D414yes—
356C2×Dic83C22×D414yes—
357C2×Dic83C2×#4114yes—
358C4×D83—416no—
359Dic166—232no—
360C22×C83—24no—
361C22×C83—24no—
362C22×C83—24no—
363C22×C83—42no—
364C22×C83—42no—
365C22×C83—42no—
366C22×C83—42no—
367C22×C83—416no—
368C22×C83C2×#12114yes—
369C22×C83#52514yes—
370C22×C83#53614yes—
371C22×C83#54814yes—
372C22×C83#54814yes—
373C22×C83#55214yes—
374C22×C83#55214yes—
375C22×C83C23×D411yescharacteristic
376C22×C83C23×D411yescharacteristic
377C22×C83C22×#4111yescharacteristic
378C22×C83C22×#4111yescharacteristic
379C22×C83C22×#4111yescharacteristic
380C22×C83C2×2−1+411yescharacteristic
381C22×C83C2×2−1+411yescharacteristic
382C2×D83—24no—
383C2×D83—24no—
384C2×D83—24no—
385C2×D83—42no—
386C2×D83—42no—
387C2×D83—42no—
388C2×D83—42no—
389C2×D83—416no—
390C4×C83—24no—
391C4×C83—24no—
392C4×C83—42no—
393C4×C83—42no—
394C4×C83—42no—
395C4×C83—42no—
396Dic83—24no—
397Dic83—24no—
398Dic83—42no—
399Dic83—42no—
400Dic83—42no—
401Dic83—42no—
402Dic83C2×#12118yes—
403C2×#2536—831nomaximal, Sylow
404C2×C83—44no—
405C2×C83#253618yescomplemented
406C2×C83C22×#12111yescharacteristic
407C2×C83C2×#52511yescharacteristic
408C2×C83C2×#53611yescharacteristic
409C2×C83C2×#54811yescharacteristic
410C2×C83C2×#54811yescharacteristic
411C2×C83C2×#55211yescharacteristic
412C2×C83C2×#55211yescharacteristic
413D83—44no—
414C22×C22⋊Q8—831no—
415C22×C22⋊Q8—831no—
416C22×C4×Q8—831no—
417C22×C4×D4—831no—
418#2536—8316no—
419C2×#398—831no—
420C2×#398—831no—
421C2×#394—831no—
422C2×#394—831no—
423C2×#388—831no—
424C2×#388—831no—
425C2×#388—831no—
426C2×#388D8311yescharacteristic, complemented
427C2×#382—831no—
428C2×#380—831no—
429C2×#380—831no—
430C83C2×#253611yescharacteristic, complemented, Sylow
431C23×Q8—831no—
432C23×D4—831no—
433C24×C4—831no—
434C24×C4—831no—
435C2×C22⋊Q8—838no—
436C2×C22⋊Q8—838no—
437C2×C22⋊Q8—1668no—
438C2×C22⋊Q8—1668no—
439C2×C4×Q8—838no—
440C2×C4×Q8—1668no—
441C2×C4×D4—838no—
442C2×C4×D4—1668no—
443C22×C4⋊C4—831no—
444C22×C4⋊C4—831no—
445C22×C4⋊C4—831no—
446C22×C4⋊C4—831no—
447C22×C4⋊C4—831no—
448C22×C4⋊C4—831no—
449C22×C4⋊C4—831no—
450C22×C4⋊C4—831no—
451C22×C4⋊C4—831no—
452C22×C4⋊C4C2×D8311yescharacteristic
453C22×C22⋊C4—831no—
454C22×C22⋊C4—831no—
455C22×C22⋊C4—831no—
456C22×C22⋊C4—831no—
457C22×C22⋊C4—831no—
458C22×C22⋊C4—831no—
459C22×C22⋊C4—831no—
460C22×C22⋊C4C2×D8311yescharacteristic
461C22×C22⋊C4C2×D8311yescharacteristic
462C22×C22⋊C4C2×D8311yescharacteristic
463C22×C42—831no—
464C22×C42—831no—
465C22×C42C2×D8311yescharacteristic
466#398—838no—
467#398—838no—
468#394—838no—
469#394—838no—
470#388—838no—
471#388—838no—
472#388—838no—
473#388C2×D8318yescomplemented
474#382—838no—
475#380—838no—
476#380—838no—
477C2×#95—831no—
478C2×#95—831no—
479C2×#95—831no—
480C2×#95—831no—
481C2×#95—831no—
482C2×#95—831no—
483C2×#95C2×D8311yescharacteristic
484C2×#95C2×D8311yescharacteristic
485C25—831no—
486C25C22×D8311yescharacteristic
487C22×Q8—838no—
488C22×Q8—834no—
489C22×Q8—1664no—
490C22×Q8—1664no—
491C22×D4—834no—
492C22×D4—1664no—
493C22×D4—1664no—
494C22×D4—1664no—
495C23×C4—831no—
496C23×C4—831no—
497C23×C4—831no—
498C23×C4—834no—
499C23×C4—831no—
500C23×C4—831no—
501C23×C4—831no—
502C23×C4—831no—
503C23×C4—834no—
504C23×C4—1664no—
505C23×C4—1664no—
506C23×C4—1664no—
507C23×C4—1664no—
508C23×C4—1664no—
509C23×C4—1664no—
510C23×C4C22×D8311yescharacteristic
511C23×C4C22×D8311yescharacteristic
512C23×C4C22×D8311yescharacteristic
513C23×C4C22×D8311yescharacteristic
514C23×C4C22×D8311yescharacteristic
515C23×C4C22×D8311yescharacteristic
516C22⋊Q8—16632no—
517C22⋊Q8—16632no—
518C4×Q8—16632no—
519C4×D4—16632no—
520C2×C4⋊C4—24no—
521C2×C4⋊C4—834no—
522C2×C4⋊C4—834no—
523C2×C4⋊C4—834no—
524C2×C4⋊C4—834no—
525C2×C4⋊C4—834no—
526C2×C4⋊C4—834no—
527C2×C4⋊C4—834no—
528C2×C4⋊C4—834no—
529C2×C4⋊C4—834no—
530C2×C4⋊C4—1664no—
531C2×C4⋊C4—1664no—
532C2×C4⋊C4—1664no—
533C2×C4⋊C4—1664no—
534C2×C4⋊C4—1664no—
535C2×C4⋊C4—1664no—
536C2×C4⋊C4—1664no—
537C2×C4⋊C4—1664no—
538C2×C4⋊C4—1664no—
539C2×C4⋊C4C22×D8314yes—
540C2×C22⋊C4—24no—
541C2×C22⋊C4—24no—
542C2×C22⋊C4—24no—
543C2×C22⋊C4—834no—
544C2×C22⋊C4—834no—
545C2×C22⋊C4—834no—
546C2×C22⋊C4—834no—
547C2×C22⋊C4—834no—
548C2×C22⋊C4—834no—
549C2×C22⋊C4—834no—
550C2×C22⋊C4—1664no—
551C2×C22⋊C4—1664no—
552C2×C22⋊C4—1664no—
553C2×C22⋊C4—1664no—
554C2×C22⋊C4—1664no—
555C2×C22⋊C4—1664no—
556C2×C22⋊C4—1664no—
557C2×C22⋊C4C22×D8314yes—
558C2×C22⋊C4C22×D8314yes—
559C2×C22⋊C4C22×D8314yes—
560C2×C42—24no—
561C2×C42—838no—
562C2×C42—834no—
563C2×C42—834no—
564C2×C42—1664no—
565C2×C42C22×D8314yes—
566#95—834no—
567#95—834no—
568#95—834no—
569#95—834no—
570#95—834no—
571#95—834no—
572#95C22×D8314yes—
573#95C22×D8314yes—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—834no—
581C24—832no—
582C24—1662no—
583C24—1662no—
584C24—1662no—
585C24—1662no—
586C24—1662no—
587C24—1662no—
588C24#1305059014yes—
589C24C23×D8312yes—
590C24C23×D8311yescharacteristic
591C2×Q8—8316no—
592C2×Q8—1668no—
593C2×Q8—16632no—
594C2×Q8—1668no—
595C2×D4—1668no—
596C2×D4—1668no—
597C2×D4—16632no—
598C2×D4—1668no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—22no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—33216no—
616C22×C4—33216no—
617C22×C4—834no—
618C22×C4—834no—
619C22×C4—834no—
620C22×C4—832no—
621C22×C4—834no—
622C22×C4—834no—
623C22×C4—832no—
624C22×C4—832no—
625C22×C4—832no—
626C22×C4—832no—
627C22×C4—832no—
628C22×C4—832no—
629C22×C4—1668no—
630C22×C4—1668no—
631C22×C4—1668no—
632C22×C4—1668no—
633C22×C4—1668no—
634C22×C4—1668no—
635C22×C4—1662no—
636C22×C4—1662no—
637C22×C4—1662no—
638C22×C4—1662no—
639C22×C4—1662no—
640C22×C4—1662no—
641C22×C4—1662no—
642C22×C4—1662no—
643C22×C4—1662no—
644C22×C4—1662no—
645C22×C4—1662no—
646C22×C4—1662no—
647C22×C4—1662no—
648C22×C4—1662no—
649C22×C4—1662no—
650C22×C4—1662no—
651C22×C4D4×D8314yes—
652C22×C4D4×D8314yes—
653C22×C4C23×D8312yes—
654C22×C4C23×D8312yes—
655C22×C4C23×D8312yes—
656C22×C4C23×D8312yes—
657C22×C4C23×D8312yes—
658C22×C4C23×D8312yes—
659C4⋊C4—28no—
660C4⋊C4—1668no—
661C4⋊C4—1668no—
662C4⋊C4—1668no—
663C4⋊C4—1668no—
664C4⋊C4—1668no—
665C4⋊C4—1668no—
666C4⋊C4—1668no—
667C4⋊C4—1668no—
668C4⋊C4—1668no—
669C22⋊C4—28no—
670C22⋊C4—28no—
671C22⋊C4—28no—
672C22⋊C4—1668no—
673C22⋊C4—1668no—
674C22⋊C4—1668no—
675C22⋊C4—1668no—
676C22⋊C4—1668no—
677C22⋊C4—1668no—
678C22⋊C4—1668no—
679C42—28no—
680C42—8316no—
681C42—1668no—
682C23—28no—
683C23—28no—
684C23—28no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—22no—
690C23—22no—
691C23—44no—
692C23—44no—
693C23—44no—
694C23—44no—
695C23—3324no—
696C23—3324no—
697C23—3324no—
698C23—3324no—
699C23—834no—
700C23—1668no—
701C23—1668no—
702C23—1668no—
703C23—1662no—
704C23—1662no—
705C23—1662no—
706C23—1662no—
707C23—1662no—
708C23—1662no—
709C23C2×D4×D8312yes—
710C23C2×D4×D8312yes—
711C23#41×D8312yes—
712C23#41×D8312yes—
713C23C2×#1305059014yes—
714C23C2×#1305059012yes—
715C23#1458183912yes—
716C23#1458183912yes—
717C23C24×D8311yescharacteristic
718Q8—16632no—
719D4—16632no—
720C2×C4—28no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—28no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—44no—
739C2×C4—44no—
740C2×C4—44no—
741C2×C4—44no—
742C2×C4—33216no—
743C2×C4—3324no—
744C2×C4—3324no—
745C2×C4—3324no—
746C2×C4—3324no—
747C2×C4—33216no—
748C2×C4—8316no—
749C2×C4—834no—
750C2×C4—834no—
751C2×C4—834no—
752C2×C4—834no—
753C2×C4—834no—
754C2×C4—1662no—
755C2×C4—1662no—
756C2×C4—1662no—
757C2×C4—1662no—
758C2×C4—1662no—
759C2×C4—1662no—
760C2×C4—1662no—
761C2×C4—1662no—
762C2×C4—1662no—
763C2×C4—1662no—
764C2×C4—1662no—
765C2×C4—1662no—
766C2×C4—1668no—
767C2×C4—1668no—
768C2×C4—1662no—
769C2×C4—1662no—
770C2×C4—1662no—
771C2×C4—1662no—
772C2×C4C2×D4×D8314yes—
773C2×C4C2×D4×D8314yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—416no—
782C22—3322no—
783C22—3322no—
784C22—3322no—
785C22—3322no—
786C22—33216no—
787C22—1664no—
788C22—1664no—
789C22—1664no—
790C22#121×D8314yes—
791C22#1912821014yes—
792C22#1912827314yes—
793C22#1912835914yes—
794C22#1912836014yes—
795C22#1912838414yes—
796C22#1912838714yes—
797C22C22×D4×D8311yescharacteristic
798C22C22×D4×D8311yescharacteristic
799C22C2×#41×D8311yescharacteristic
800C22C2×#41×D8311yescharacteristic
801C22C22×#1305059011yescharacteristic
802C22C2×#1458183911yescharacteristic
803C22C2×#1458183911yescharacteristic
804C4—24no—
805C4—24no—
806C4—42no—
807C4—42no—
808C4—42no—
809C4—42no—
810C4—3322no—
811C4—3322no—
812C4—3322no—
813C4—3322no—
814C4—838no—
815C4—1664no—
816C4—1664no—
817C2—44no—
818C2—3324no—
819C2#2491237118yesdirect product factor
820C2C2×#121×D8311yescharacteristic
821C2C2×#1912821011yescharacteristic
822C2C2×#1912827311yescharacteristic
823C2C2×#1912835911yescharacteristic
824C2C2×#1912836011yescharacteristic
825C2C2×#1912838411yescharacteristic
826C2C2×#1912838711yescharacteristic
subgroupG/H
centerC24C23×D83
commutator, cosocleC23×C83C25
FrattiniC23C24×D83
FittingC2×#388×C83C2
socleC24×C83C24
prime radicalC23×C22⋊D83C22
hypercenterC2×#388D83
hypocenterC83C2×#2536
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C24 ◁ C2×#388

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×#14581770C2semidirect
2. C22×#14581769C2semidirect
3. C22×C4×Dic166C2semidirect
5. #24912371C2direct (N × H)
6. C2×#19127635C2semidirect
7. C2×#19127634C2semidirect
10. C2×#19127593C2semidirect
11. C2×#19127592C2semidirect
12. C2×#19127589C2semidirect
13. C2×#19127565C2semidirect
14. C2×#19127560C2semidirect
15. C2×#19127559C2semidirect
16. C2×#388×C83C2semidirect
22. C2×#14581770C22semidirect
24. C2×#14581769C22semidirect
26. C2×C4×Dic166C22semidirect
47. #19127635C22semidirect
48. #19127634C22semidirect
51. #19127593C22semidirect
52. #19127592C22semidirect
53. #19127589C22semidirect
54. #19127565C22semidirect
55. #19127560C22semidirect
56. #19127559C22semidirect
68. #388×C83C22semidirect
74. C22×Dic166D4semidirect
171. C2×Dic166C2×D4semidirect
405. C2×C83#2536semidirect
426. C2×#388D83semidirect
430. C83C2×#2536semidirect
473. #388C2×D83semidirect
819. C2#24912371direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×#145817702
C22×#145817692
C22×C4×Dic1662
C22×(C22⋊D83)⋊C42
#249123712
C2×#191276352
C2×#191276342
C2×#191276172
C2×#191276162
C2×#191275932
C2×#191275922
C2×#191275892
C2×#191275652
C2×#191275602
C2×#191275592
C2×#388×C832
C2×#253683